• The Pure and Applied Mathematics
• /
• v.14 no.2 s.36
• /
• pp.99-109
• /
• 2007

Being complicated in computation, iteration of a nonlinear 1-dimensional mapping makes many interesting problems, one of which is about the change of the number of vertices under iteration. In this paper we investigate iteration of polygonal functions which each have only one vertex and give conditions under which the number of vertices either does not increase or has a bound under iteration.

• Kyungpook Mathematical Journal
• /
• v.59 no.3
• /
• pp.445-464
• /
• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.651-675
• /
• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.177-195
• /
• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.1-11
• /
• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.961-969
• /
• 2021

In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.785-795
• /
• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.3
• /
• pp.671-684
• /
• 2023

In this paper, we prove the generalized Hyers-Ulam stability of a general quintic functional equation, $\sum\limits_{k=0}^{6}(-1)^k{_6}C_kf(x+(3-k)y)=0$, by using the fixed point method.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.309-322
• /
• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.2
• /
• pp.517-526
• /
• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.